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  • 1
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Macromolecules 28 (1995), S. 4013-4019 
    ISSN: 1520-5835
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 93 (1990), S. 7148-7152 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We study the bimolecular annihilation reaction A+B→0 with immobile reactants interacting via exchange. We extend our previous analyses to the case of unequal concentrations of A and B particles. A comparison between the direct simulation of the reaction process and an analytical approach, which is based on Kirkwood's superposition approximation, shows reasonable agreement, although deviations are larger than in the case of equal A and B concentrations. Interestingly, the asymptotic decay forms for the particle concentrations (when formulated in terms of a suitable reaction length) parallel those encountered in diffusion-limited reactions. Here the diffusion length lD=(Dt)1/2 gets replaced by the reaction radius ξ=ln t. We discuss implications of this finding for a qualitative (but quite accurate) picture of the temporal evolution behavior.
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 93 (1990), S. 7471-7475 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A phenomenological approach, which takes into account the basic geometry and the topology of fractal lattices and of branched polymers, is used to derive a new expression for the Flory exponent describing the average radius of gyration of branched polymers on fractals. The mean-field version of this formula nicely reproduces the values of the Flory exponent, calculated using real-space renormalization group methods on several fractal lattices. This technique also allows the determination of the scaling exponent of the radius of gyration of branched polymers without excluded-volume interactions on fractal lattices. As an application, the findings are exemplified by analyzing the direct, incoherent energy transfer (via multipolar interactions and exchange) from excited donors to acceptors, which are attached to branched polymers.
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  • 4
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 93 (1990), S. 3685-3692 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A computer simulation for the heterogeneous catalyzed oxidation of CO is presented. The simulation includes adsorption, CO diffusion, reaction, and CO2 desorption. It is found that a first-order phase transition occurs at yCO=y2 (yCO is the mole fraction of CO in the gas phase). In the interval [ y2,1], the catalyst is almost completely covered with CO, i.e., the catalyst is poisoned. The value of y2 is a function of the adsorption/diffusion ration. For no CO diffusion, Ziff, Gulary, and Barshad [Phys. Rev. Lett. 24, 2553 (1986)] found y2=0.525. In this paper, for A/D=1/40, y2=0.650. In a mean-field ansatz with infinite diffusion rate, one obtains y2=0.666. With a linear stability analysis, the dependence of y2 on different initial coverage values can be explained. An initial coverage of oxygen does not influence the value of y2, but with increasing initial coverage of CO, the value of y2 decreases. It will be shown that oscillations are not possible in this simple reaction system. The adsorbed O atoms form large clusters that are found to be fractal in nature. The fractal dimension Df is equal to 1.88. A percolation transition at yCO=0.520 is observed, which corresponds to a critical oxygen coverage of aitch-thetaO,crit.=0.561. At this oxygen coverage, an infinite cluster percolates through the lattice. The value of aitch-thetaO,crit. is nearly independent of the A/D ratio. In correlated percolation simulations, it is found that aitch-thetaO,crit.=0.559, which is in good agreement with the value obtained from the reaction system.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 92 (1990), S. 2310-2316 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We study the bimolecular annihilation reaction A+B→0 with immobile reactants in arbitrary dimension. For this we derive a closed set of integrodifferential equations by using Kirkwood's superposition approximation to decouple the infinite hierarchy of equations for the many-center correlation functions. We find that for exchange-type interactions and equal numbers of A and B species the reactant concentration n decays as n∼ξ−d/2, where ξ is time-dependent, ξ=ln t, and may be interpreted to be an effective reaction radius. A comparison to numerical simulations shows very good agreement to the theoretical expressions, both for the temporal evolution of particle concentrations and also for the pair-correlation functions; this confirms the validity of the superposition approximation.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 4353-4359 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In this work we study the direct, incoherent energy transfer from excited donors to acceptors, which are attached to chainlike polymers. We consider both multipolar and exchange-type interactions between the donors and the acceptors. The polymers are modeled through random walks (Gaussian or self-avoiding, depending on the solvent). With the use of the end-to-end distribution function of the walks, we calculate the time dependence of the ensemble averaged decay of the excitation of the donor. For multipolar and exchange-type interactions, we find Kohlrausch–Williams–Watts (KWW) stretched exponential and exponential–logarithmic decay patterns, respectively. The decay forms reflect the quality (good or poor) of the solvent directly and they may be used to test transitions in the polymer conformation.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 117 (2002), S. 2474-2480 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We investigate on small world networks (SWN's) the survival probability of immobile targets, which get annihilated by random walkers at first encounter. On SWN's we find (distinct from regular lattices, Cayley trees, and regular ultrametric spaces) that in general the survival probability cannot be directly related to the average number of distinct sites visited. We underline this finding with arguments related to the structural disorder of SWN's and through the derivation of a lower bound for the targets' decay. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 116 (2002), S. 2636-2641 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The mechanical and dielectric relaxation of polymer networks depends (especially in simple Gaussian-type approaches which extend the Rouse model) on the eigenvalues of the corresponding connectivity matrices. We use this to evaluate explicitly experimentally accessible relaxation forms for finite Sierpinski-type networks, whose eigenvalue spectra are multifractal. It turns out that the observable quantities are by far less singular than the eigenvalue spectra, since the underlying spectral structures get smoothed out. Our results establish unequivocally the spectral dimension as fundamental relaxation parameter; to see this, however, the finite fractal networks have to be sufficiently large. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 116 (2002), S. 8616-8624 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We focus on the dynamical properties of dendrimers and of randomly built branched polymers, which allows us to assess theoretically the role of disorder on the relaxation forms. We model the random polymers through a stochastic growth algorithm. Our studies are carried out both in the Rouse and also in the Zimm framework; the latter accounts for hydrodynamic interactions. Moreover, we also mimic the local geometry by imposing conditions on the average values of the angles between neighboring segments. Excluded volume interactions, however, are neglected throughout. The storage G′(ω) and the loss G″(ω) moduli, which we calculate, turn out to depend more on the hydrodynamic and the angular restrictions than on randomness. Furthermore, we find that both the randomness and the angular restrictions slow down the relaxation. Given that G′(ω), G″(ω) and also C(t), a function related to the radius of gyration, are all connected to the relaxation function G(t), a fact which we recall, we also calculate numerically G(t) and C(t); moreover we fit, following previous works, C(t) to stretched-exponential forms. Interestingly, it appears that from all functions considered G(t) is most sensitive to disorder. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Physica A: Statistical Mechanics and its Applications 168 (1990), S. 637-645 
    ISSN: 0378-4371
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Physics
    Type of Medium: Electronic Resource
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